Lawrence Markus will carry out investigations into stochastic differential equations and into the control of hybrid systems in infinite dimensional state spaces. The former work arises from a formulation of relativistic Brownian motion as a stochastic dynamical system on a manifold. These are in turn related to geodesic flows which will be the focus of Markus' attention in this area. A hybrid system is a combination of a system such as an elastic beam governed by a partial differential equation and a rigid body governed by an ordinary differential equation. This combination will be controlled by boundary controllers acting only in the rigid body. Investigations such as these are important because of their applicability to the problem of controlling large scale space structures. George Sell will work on inertial manifolds for nonlinear evolutionary equations, functional differential equations with feedback, spectral properties of linear evolutionary equations, and chaotic behavior for the perturbed sine-Gordon equation. Inertial manifolds are currently being investigated by many researchers with the aim of using them to investigate the global attractors of nonlinear dissipative evolutionary equations. Markus and Sell will be joined by Yuncheng You, who will work with them principally in the areas of control of large space structures and control theory of differentiable manifolds.
